# theory of computation

> subfield of computer science

**Wikidata**: [Q844718](https://www.wikidata.org/wiki/Q844718)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Theory_of_computation)  
**Source**: https://4ort.xyz/entity/theory-of-computation

## Summary
The theory of computation is a subfield of computer science that studies the principles and models underlying computation, including what can be computed, how efficiently it can be done, and the abstract frameworks that define computational processes. It is foundational to understanding the capabilities and limitations of algorithms and computational systems.

## Key Facts
- **Classification**: It is classified as a subfield of computer science.
- **Parent Fields**: It is part of theoretical computer science, computer science, and mathematics.
- **Related Fields**: Closely related to computability theory, algorithmics, and lambda calculus.
- **Aliases**: Also known as the theory of algorithms.
- **Subclass Of**: academic discipline, formal science.
- **Distinct From**: Information science, informatics, and computational science.
- **Practiced By**: Theoretical computer scientists, mathematicians, and computer scientists.
- **Notable Individuals**: Richard M. Karp, Stephen Cole Kleene, Alexander Razborov, and others have made foundational contributions.
- **Library Classification**: Assigned the Dewey Decimal Classification number 004 and Universal Decimal Classification 004.
- **Wikipedia Title**: "Theory of computation".
- **Wikidata Description**: Subfield of computer science.
- **Identifiers**: 
  - P373: Theory of computation
  - P646: /m/07h44
  - P1296: 0267888
  - P2581: 02392561n
  - P2924: 1810389
  - P3417: Theory-of-Computation
  - P3553: 19599016
  - P3847: theory_of_computation
  - P6366: 24858836
  - P7554: Algorithms,_theory_of, Mathematical_theory_of_computation
  - P7666: algoritmu-teorija
  - P8529: 4613, 461399
  - P10037: teoria-della-computazione
  - P10283: C24858836
  - P11514: teoriia-algoritmov-cd3bb5
  - P12385: teoria-de-la-computacio
- **Related Entities**: 
  - computability theory
  - algorithmics
  - lambda calculus
  - academic discipline
  - theory
  - Richard M. Karp
  - Stephen Cole Kleene
  - Pyotr Novikov
  - Alexander Razborov
  - Anatoly Karatsuba
  - George Bernard Dantzig

## FAQs
### What is the theory of computation?
The theory of computation is a subfield of computer science that studies the principles and models underlying computation, including what can be computed, how efficiently it can be done, and the abstract frameworks that define computational processes. It is foundational to understanding the capabilities and limitations of algorithms and computational systems.

### What are the main branches or components of the theory of computation?
The theory of computation includes subfields such as computability theory, algorithmics, and lambda calculus. It is part of theoretical computer science and is closely related to the study of algorithms and data structures.

### Who are some notable figures associated with the theory of computation?
Notable individuals include Richard M. Karp, Stephen Cole Kleene, Alexander Razborov, and George Bernard Dantzig. These individuals have made foundational contributions to the field, particularly in areas like computational complexity and recursion theory.

### How is the theory of computation classified in academic and library systems?
It is classified under the Dewey Decimal Classification number 004 and Universal Decimal Classification 004. It is also categorized as a subfield of computer science and theoretical computer science.

### What is the relationship between the theory of computation and computability theory?
Computability theory is a core component of the theory of computation, focusing on what problems can be solved by algorithms and the inherent limitations of computation.

### What distinguishes the theory of computation from information science?
The theory of computation is distinct from information science, which focuses on the analysis, collection, classification, manipulation, storage, retrieval, and dissemination of information. The former is more focused on the abstract principles of computation, while the latter is concerned with information systems and processes.

## Why It Matters
The theory of computation is significant because it provides the theoretical foundation for understanding what can and cannot be computed, guiding the development of algorithms, programming languages, and computational systems. It plays a critical role in shaping modern computer science by defining the limits and capabilities of computation. Its principles underpin numerous fields, including artificial intelligence, data science, and software engineering, making it essential for innovations in technology.

## Notable For
- **Foundational Role**: It serves as the core theoretical framework for computer science, defining what is computable and how efficiently it can be done.
- **Interdisciplinary Reach**: It bridges gaps between mathematics, logic, and computer science, influencing fields like artificial intelligence and data science.
- **Influence on Computation**: It provides the basis for algorithm design, programming languages, and computational complexity.
- **Historical Contributions**: Pioneers like Stephen Cole Kleene and Richard M. Karp have made foundational contributions that continue to shape the field.
- **Academic Rigor**: It is formally classified as an academic discipline and a formal science, distinct from natural or social sciences.

## Body

### Definition and Scope
The theory of computation is a subfield of computer science that studies the principles and models underlying computation. It encompasses:
- **Computability theory**, which explores what problems can be solved by algorithms.
- **Algorithmics**, which focuses on the study of algorithms and data structures.
- **Lambda calculus**, a formal system in mathematical logic for expressing computation.

It is distinct from information science, informatics, and computational science, focusing specifically on the theoretical aspects of computation.

### Classification and Relationships
The theory of computation is:
- **Part of**: Theoretical computer science, computer science, and mathematics.
- **Related to**: Computability theory, algorithmics, and lambda calculus.
- **Distinct from**: Information science, informatics, and computational science.

It is classified under the Dewey Decimal Classification number 004 and Universal Decimal Classification 004.

### Key Individuals and Contributions
Several notable individuals have made significant contributions to the theory of computation:
- **Richard M. Karp** is known for his work in combinatorial algorithms and computational complexity.
- **Stephen Cole Kleene** developed foundational concepts in recursion theory and formal logic, including the Kleene star.
- **Alexander Razborov** is recognized for his work in computational complexity theory, particularly the "Natural Proofs" barrier.
- **George Bernard Dantzig** contributed to optimization theory with the simplex algorithm.

### Academic and Theoretical Impact
The theory of computation has had a profound impact on:
- **Algorithm Design**: Providing frameworks for understanding the efficiency and limitations of algorithms.
- **Programming Languages**: Influencing the development of formal languages and compilers.
- **Computational Complexity**: Defining the resources required to solve computational problems.

### Educational and Research Applications
The field is foundational in:
- **Computer Science Education**: It is a core subject in academic curricula, shaping the next generation of computer scientists.
- **Research and Innovation**: It drives advancements in artificial intelligence, data science, and software engineering.

### Community and Influence
The theory of computation has a robust academic community supported by:
- **Academic Projects**: Dedicated research initiatives and collaborations.
- **Publications**: Influential textbooks and research papers that guide the field.
- **Professional Recognition**: Awards and honors for pioneering work, such as the Turing Award and the National Medal of Science.

### Legacy and Ongoing Relevance
The theory of computation continues to evolve, with:
- **Foundational Research**: Ongoing contributions to understanding the limits and capabilities of computation.
- **Interdisciplinary Applications**: Influence on fields like artificial intelligence, operations research, and data science.
- **Educational Resources**: Textbooks and academic materials that educate and inspire future researchers.

The field's principles underpin modern computational systems, ensuring its continued relevance in a rapidly advancing technological landscape.

## References

1. Freebase Data Dumps. 2013
2. BabelNet
3. Quora
4. [Source](https://vocabs.ardc.edu.au/viewById/316)
5. [OpenAlex](https://docs.openalex.org/download-snapshot/snapshot-data-format)